A healthy combination of both is the obvious answer for me.
Edit; Rol: would the core gamer enjoy and spend a lot of time with Wii Fit (on average) and would the casual gamer enjoy and spend a lot of time with RPG's and FPS games (on average)? Likely not. People who only play Angry Birds on iPhone or Nintendogs will probably not be in the demographic of Portal 2 and someone who spends his entire life immersed in a MMO will probably care little for feebleminded mingames with no apparent objective and substance.
Gamers are very different (which you also state yourself) and I can easily see "core" and "casual" as two separate markets. Your grandparents' generation are unlikely to buy Gran Turismo 5 for instance, or do people still claim that casual games draw people into and drive them towards "heavier" stuff? Someone who is not quite taken with gaming as a hobby and time consumer will never ever sit down and start playing Neverwinter Nights 2 all of the sudden.
